The asymptotic form of the Bayes acceptance region is derived for testing simple null-hypotheses in multiparameter exponential families. This result suggests a reasonable definition for tests which might be called "almost-Bayes". The rate at which the risk of the Bayes test converges to zero is obtained, showing the nature of its dependence on the prior distribution and providing a basis for comparison of almost-Bayes procedures. Concluding remarks contain a brief discussion of some asymptotic consequences of poor prior guessing.
@article{1176344129,
author = {Johnson, B. R. and Traux, D. R.},
title = {Asymptotic Behavior of Bayes Procedures for Testing Simple Hypotheses in Multiparameter Exponential Families},
journal = {Ann. Statist.},
volume = {6},
number = {1},
year = {1978},
pages = { 346-361},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344129}
}
Johnson, B. R.; Traux, D. R. Asymptotic Behavior of Bayes Procedures for Testing Simple Hypotheses in Multiparameter Exponential Families. Ann. Statist., Tome 6 (1978) no. 1, pp. 346-361. http://gdmltest.u-ga.fr/item/1176344129/